2 <indexterm><primary>language, GHC</primary></indexterm>
3 <indexterm><primary>extensions, GHC</primary></indexterm>
4 As with all known Haskell systems, GHC implements some extensions to
5 the language. To use them, you'll need to give a <option>-fglasgow-exts</option>
6 <indexterm><primary>-fglasgow-exts option</primary></indexterm> option.
10 Virtually all of the Glasgow extensions serve to give you access to
11 the underlying facilities with which we implement Haskell. Thus, you
12 can get at the Raw Iron, if you are willing to write some non-standard
13 code at a more primitive level. You need not be “stuck” on
14 performance because of the implementation costs of Haskell's
15 “high-level” features—you can always code “under” them. In an extreme case, you can write all your time-critical code in C, and then just glue it together with Haskell!
19 Before you get too carried away working at the lowest level (e.g.,
20 sloshing <literal>MutableByteArray#</literal>s around your
21 program), you may wish to check if there are libraries that provide a
22 “Haskellised veneer” over the features you want. The
23 separate libraries documentation describes all the libraries that come
27 <!-- LANGUAGE OPTIONS -->
28 <sect1 id="options-language">
29 <title>Language options</title>
31 <indexterm><primary>language</primary><secondary>option</secondary>
33 <indexterm><primary>options</primary><secondary>language</secondary>
35 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
38 <para> These flags control what variation of the language are
39 permitted. Leaving out all of them gives you standard Haskell
45 <term><option>-fglasgow-exts</option>:</term>
46 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
48 <para>This simultaneously enables all of the extensions to
49 Haskell 98 described in <xref
50 linkend="ghc-language-features">, except where otherwise
56 <term><option>-ffi</option> and <option>-fffi</option>:</term>
57 <indexterm><primary><option>-ffi</option></primary></indexterm>
58 <indexterm><primary><option>-fffi</option></primary></indexterm>
60 <para>This option enables the language extension defined in the
61 Haskell 98 Foreign Function Interface Addendum plus deprecated
62 syntax of previous versions of the FFI for backwards
68 <term><option>-fwith</option>:</term>
69 <indexterm><primary><option>-fwith</option></primary></indexterm>
71 <para>This option enables the deprecated <literal>with</literal>
72 keyword for implicit parameters; it is merely provided for backwards
74 It is independent of the <option>-fglasgow-exts</option>
80 <term><option>-fno-monomorphism-restriction</option>:</term>
81 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
83 <para> Switch off the Haskell 98 monomorphism restriction.
84 Independent of the <option>-fglasgow-exts</option>
90 <term><option>-fallow-overlapping-instances</option></term>
91 <term><option>-fallow-undecidable-instances</option></term>
92 <term><option>-fallow-incoherent-instances</option></term>
93 <term><option>-fcontext-stack</option></term>
94 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
95 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
96 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
98 <para> See <xref LinkEnd="instance-decls">. Only relevant
99 if you also use <option>-fglasgow-exts</option>.</para>
104 <term><option>-finline-phase</option></term>
105 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
107 <para>See <xref LinkEnd="rewrite-rules">. Only relevant if
108 you also use <option>-fglasgow-exts</option>.</para>
113 <term><option>-fgenerics</option></term>
114 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
116 <para>See <xref LinkEnd="generic-classes">. Independent of
117 <option>-fglasgow-exts</option>.</para>
122 <term><option>-fno-implicit-prelude</option></term>
124 <para><indexterm><primary>-fno-implicit-prelude
125 option</primary></indexterm> GHC normally imports
126 <filename>Prelude.hi</filename> files for you. If you'd
127 rather it didn't, then give it a
128 <option>-fno-implicit-prelude</option> option. The idea
129 is that you can then import a Prelude of your own. (But
130 don't call it <literal>Prelude</literal>; the Haskell
131 module namespace is flat, and you must not conflict with
132 any Prelude module.)</para>
134 <para>Even though you have not imported the Prelude, most of
135 the built-in syntax still refers to the built-in Haskell
136 Prelude types and values, as specified by the Haskell
137 Report. For example, the type <literal>[Int]</literal>
138 still means <literal>Prelude.[] Int</literal>; tuples
139 continue to refer to the standard Prelude tuples; the
140 translation for list comprehensions continues to use
141 <literal>Prelude.map</literal> etc.</para>
143 <para>However, <option>-fno-implicit-prelude</option> does
144 change the handling of certain built-in syntax: see
145 <xref LinkEnd="rebindable-syntax">.</para>
153 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
154 <!-- included from primitives.sgml -->
158 <!-- TYPE SYSTEM EXTENSIONS -->
159 <sect1 id="type-extensions">
160 <title>Type system extensions</title>
162 <sect2 id="nullary-types">
163 <title>Data types with no constructors</title>
165 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
166 a data type with no constructors. For example:</para>
170 data T a -- T :: * -> *
173 <para>Syntactically, the declaration lacks the "= constrs" part. The
174 type can be parameterised over types of any kind, but if the kind is
175 not <literal>*</literal> then an explicit kind annotation must be used
176 (see <xref linkend="sec-kinding">).</para>
178 <para>Such data types have only one value, namely bottom.
179 Nevertheless, they can be useful when defining "phantom types".</para>
182 <sect2 id="infix-tycons">
183 <title>Infix type constructors</title>
186 GHC allows type constructors to be operators, and to be written infix, very much
187 like expressions. More specifically:
190 A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
191 The lexical syntax is the same as that for data constructors.
194 Types can be written infix. For example <literal>Int :*: Bool</literal>.
198 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
199 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
202 Fixities may be declared for type constructors just as for data constructors. However,
203 one cannot distinguish between the two in a fixity declaration; a fixity declaration
204 sets the fixity for a data constructor and the corresponding type constructor. For example:
208 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
209 and similarly for <literal>:*:</literal>.
210 <literal>Int `a` Bool</literal>.
213 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
216 Data type and type-synonym declarations can be written infix. E.g.
218 data a :*: b = Foo a b
219 type a :+: b = Either a b
223 The only thing that differs between operators in types and operators in expressions is that
224 ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
225 are not allowed in types. Reason: the uniform thing to do would be to make them type
226 variables, but that's not very useful. A less uniform but more useful thing would be to
227 allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
228 lists. So for now we just exclude them.
235 <sect2 id="class-method-types">
236 <title>Class method types
239 Haskell 98 prohibits class method types to mention constraints on the
240 class type variable, thus:
243 fromList :: [a] -> s a
244 elem :: Eq a => a -> s a -> Bool
246 The type of <literal>elem</literal> is illegal in Haskell 98, because it
247 contains the constraint <literal>Eq a</literal>, constrains only the
248 class type variable (in this case <literal>a</literal>).
251 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
256 <sect2 id="multi-param-type-classes">
257 <title>Multi-parameter type classes
261 This section documents GHC's implementation of multi-parameter type
262 classes. There's lots of background in the paper <ULink
263 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
264 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
269 I'd like to thank people who reported shorcomings in the GHC 3.02
270 implementation. Our default decisions were all conservative ones, and
271 the experience of these heroic pioneers has given useful concrete
272 examples to support several generalisations. (These appear below as
273 design choices not implemented in 3.02.)
277 I've discussed these notes with Mark Jones, and I believe that Hugs
278 will migrate towards the same design choices as I outline here.
279 Thanks to him, and to many others who have offered very useful
287 There are the following restrictions on the form of a qualified
294 forall tv1..tvn (c1, ...,cn) => type
300 (Here, I write the "foralls" explicitly, although the Haskell source
301 language omits them; in Haskell 1.4, all the free type variables of an
302 explicit source-language type signature are universally quantified,
303 except for the class type variables in a class declaration. However,
304 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
313 <emphasis>Each universally quantified type variable
314 <literal>tvi</literal> must be mentioned (i.e. appear free) in <literal>type</literal></emphasis>.
316 The reason for this is that a value with a type that does not obey
317 this restriction could not be used without introducing
318 ambiguity. Here, for example, is an illegal type:
322 forall a. Eq a => Int
326 When a value with this type was used, the constraint <literal>Eq tv</literal>
327 would be introduced where <literal>tv</literal> is a fresh type variable, and
328 (in the dictionary-translation implementation) the value would be
329 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
330 can never know which instance of <literal>Eq</literal> to use because we never
331 get any more information about <literal>tv</literal>.
338 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
339 universally quantified type variables <literal>tvi</literal></emphasis>.
341 For example, this type is OK because <literal>C a b</literal> mentions the
342 universally quantified type variable <literal>b</literal>:
346 forall a. C a b => burble
350 The next type is illegal because the constraint <literal>Eq b</literal> does not
351 mention <literal>a</literal>:
355 forall a. Eq b => burble
359 The reason for this restriction is milder than the other one. The
360 excluded types are never useful or necessary (because the offending
361 context doesn't need to be witnessed at this point; it can be floated
362 out). Furthermore, floating them out increases sharing. Lastly,
363 excluding them is a conservative choice; it leaves a patch of
364 territory free in case we need it later.
374 These restrictions apply to all types, whether declared in a type signature
379 Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
380 the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
387 f :: Eq (m a) => [m a] -> [m a]
394 This choice recovers principal types, a property that Haskell 1.4 does not have.
400 <title>Class declarations</title>
408 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
412 class Collection c a where
413 union :: c a -> c a -> c a
424 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
425 of "acyclic" involves only the superclass relationships. For example,
431 op :: D b => a -> b -> b
434 class C a => D a where { ... }
438 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
439 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
440 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
447 <emphasis>There are no restrictions on the context in a class declaration
448 (which introduces superclasses), except that the class hierarchy must
449 be acyclic</emphasis>. So these class declarations are OK:
453 class Functor (m k) => FiniteMap m k where
456 class (Monad m, Monad (t m)) => Transform t m where
457 lift :: m a -> (t m) a
466 <emphasis>In the signature of a class operation, every constraint
467 must mention at least one type variable that is not a class type
474 class Collection c a where
475 mapC :: Collection c b => (a->b) -> c a -> c b
479 is OK because the constraint <literal>(Collection a b)</literal> mentions
480 <literal>b</literal>, even though it also mentions the class variable
481 <literal>a</literal>. On the other hand:
486 op :: Eq a => (a,b) -> (a,b)
490 is not OK because the constraint <literal>(Eq a)</literal> mentions on the class
491 type variable <literal>a</literal>, but not <literal>b</literal>. However, any such
492 example is easily fixed by moving the offending context up to the
497 class Eq a => C a where
502 A yet more relaxed rule would allow the context of a class-op signature
503 to mention only class type variables. However, that conflicts with
504 Rule 1(b) for types above.
511 <emphasis>The type of each class operation must mention <emphasis>all</emphasis> of
512 the class type variables</emphasis>. For example:
518 insert :: s -> a -> s
522 is not OK, because the type of <literal>empty</literal> doesn't mention
523 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
524 types, and has the same motivation.
526 Sometimes, offending class declarations exhibit misunderstandings. For
527 example, <literal>Coll</literal> might be rewritten
533 insert :: s a -> a -> s a
537 which makes the connection between the type of a collection of
538 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
539 Occasionally this really doesn't work, in which case you can split the
547 class CollE s => Coll s a where
548 insert :: s -> a -> s
561 <sect3 id="instance-decls">
562 <title>Instance declarations</title>
570 <emphasis>Instance declarations may not overlap</emphasis>. The two instance
575 instance context1 => C type1 where ...
576 instance context2 => C type2 where ...
580 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify
582 However, if you give the command line option
583 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
584 option</primary></indexterm> then overlapping instance declarations are permitted.
585 However, GHC arranges never to commit to using an instance declaration
586 if another instance declaration also applies, either now or later.
592 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
598 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
599 (but not identical to <literal>type1</literal>), or vice versa.
603 Notice that these rules
608 make it clear which instance decl to use
609 (pick the most specific one that matches)
616 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
617 Reason: you can pick which instance decl
618 "matches" based on the type.
623 However the rules are over-conservative. Two instance declarations can overlap,
624 but it can still be clear in particular situations which to use. For example:
626 instance C (Int,a) where ...
627 instance C (a,Bool) where ...
629 These are rejected by GHC's rules, but it is clear what to do when trying
630 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
631 cannot apply. Yell if this restriction bites you.
634 GHC is also conservative about committing to an overlapping instance. For example:
636 class C a where { op :: a -> a }
637 instance C [Int] where ...
638 instance C a => C [a] where ...
640 f :: C b => [b] -> [b]
643 From the RHS of f we get the constraint <literal>C [b]</literal>. But
644 GHC does not commit to the second instance declaration, because in a paricular
645 call of f, b might be instantiate to Int, so the first instance declaration
646 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
647 GHC will instead silently pick the second instance, without complaining about
648 the problem of subsequent instantiations.
651 Regrettably, GHC doesn't guarantee to detect overlapping instance
652 declarations if they appear in different modules. GHC can "see" the
653 instance declarations in the transitive closure of all the modules
654 imported by the one being compiled, so it can "see" all instance decls
655 when it is compiling <literal>Main</literal>. However, it currently chooses not
656 to look at ones that can't possibly be of use in the module currently
657 being compiled, in the interests of efficiency. (Perhaps we should
658 change that decision, at least for <literal>Main</literal>.)
665 <emphasis>There are no restrictions on the type in an instance
666 <emphasis>head</emphasis>, except that at least one must not be a type variable</emphasis>.
667 The instance "head" is the bit after the "=>" in an instance decl. For
668 example, these are OK:
672 instance C Int a where ...
674 instance D (Int, Int) where ...
676 instance E [[a]] where ...
680 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
681 For example, this is OK:
685 instance Stateful (ST s) (MutVar s) where ...
689 The "at least one not a type variable" restriction is to ensure that
690 context reduction terminates: each reduction step removes one type
691 constructor. For example, the following would make the type checker
692 loop if it wasn't excluded:
696 instance C a => C a where ...
700 There are two situations in which the rule is a bit of a pain. First,
701 if one allows overlapping instance declarations then it's quite
702 convenient to have a "default instance" declaration that applies if
703 something more specific does not:
712 Second, sometimes you might want to use the following to get the
713 effect of a "class synonym":
717 class (C1 a, C2 a, C3 a) => C a where { }
719 instance (C1 a, C2 a, C3 a) => C a where { }
723 This allows you to write shorter signatures:
735 f :: (C1 a, C2 a, C3 a) => ...
739 I'm on the lookout for a simple rule that preserves decidability while
740 allowing these idioms. The experimental flag
741 <option>-fallow-undecidable-instances</option><indexterm><primary>-fallow-undecidable-instances
742 option</primary></indexterm> lifts this restriction, allowing all the types in an
743 instance head to be type variables.
750 <emphasis>Unlike Haskell 1.4, instance heads may use type
751 synonyms</emphasis>. As always, using a type synonym is just shorthand for
752 writing the RHS of the type synonym definition. For example:
756 type Point = (Int,Int)
757 instance C Point where ...
758 instance C [Point] where ...
762 is legal. However, if you added
766 instance C (Int,Int) where ...
770 as well, then the compiler will complain about the overlapping
771 (actually, identical) instance declarations. As always, type synonyms
772 must be fully applied. You cannot, for example, write:
777 instance Monad P where ...
781 This design decision is independent of all the others, and easily
782 reversed, but it makes sense to me.
789 <emphasis>The types in an instance-declaration <emphasis>context</emphasis> must all
790 be type variables</emphasis>. Thus
794 instance C a b => Eq (a,b) where ...
802 instance C Int b => Foo b where ...
806 is not OK. Again, the intent here is to make sure that context
807 reduction terminates.
809 Voluminous correspondence on the Haskell mailing list has convinced me
810 that it's worth experimenting with a more liberal rule. If you use
811 the flag <option>-fallow-undecidable-instances</option> can use arbitrary
812 types in an instance context. Termination is ensured by having a
813 fixed-depth recursion stack. If you exceed the stack depth you get a
814 sort of backtrace, and the opportunity to increase the stack depth
815 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
828 <sect2 id="implicit-parameters">
829 <title>Implicit parameters
832 <para> Implicit paramters are implemented as described in
833 "Implicit parameters: dynamic scoping with static types",
834 J Lewis, MB Shields, E Meijer, J Launchbury,
835 27th ACM Symposium on Principles of Programming Languages (POPL'00),
838 <para>(Most of the following, stil rather incomplete, documentation is due to Jeff Lewis.)</para>
840 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
841 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
842 context. In Haskell, all variables are statically bound. Dynamic
843 binding of variables is a notion that goes back to Lisp, but was later
844 discarded in more modern incarnations, such as Scheme. Dynamic binding
845 can be very confusing in an untyped language, and unfortunately, typed
846 languages, in particular Hindley-Milner typed languages like Haskell,
847 only support static scoping of variables.
850 However, by a simple extension to the type class system of Haskell, we
851 can support dynamic binding. Basically, we express the use of a
852 dynamically bound variable as a constraint on the type. These
853 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
854 function uses a dynamically-bound variable <literal>?x</literal>
855 of type <literal>t'</literal>". For
856 example, the following expresses the type of a sort function,
857 implicitly parameterized by a comparison function named <literal>cmp</literal>.
859 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
861 The dynamic binding constraints are just a new form of predicate in the type class system.
864 An implicit parameter is introduced by the special form <literal>?x</literal>,
865 where <literal>x</literal> is
866 any valid identifier. Use if this construct also introduces new
867 dynamic binding constraints. For example, the following definition
868 shows how we can define an implicitly parameterized sort function in
869 terms of an explicitly parameterized <literal>sortBy</literal> function:
871 sortBy :: (a -> a -> Bool) -> [a] -> [a]
873 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
876 Dynamic binding constraints behave just like other type class
877 constraints in that they are automatically propagated. Thus, when a
878 function is used, its implicit parameters are inherited by the
879 function that called it. For example, our <literal>sort</literal> function might be used
880 to pick out the least value in a list:
882 least :: (?cmp :: a -> a -> Bool) => [a] -> a
883 least xs = fst (sort xs)
885 Without lifting a finger, the <literal>?cmp</literal> parameter is
886 propagated to become a parameter of <literal>least</literal> as well. With explicit
887 parameters, the default is that parameters must always be explicit
888 propagated. With implicit parameters, the default is to always
892 An implicit parameter differs from other type class constraints in the
893 following way: All uses of a particular implicit parameter must have
894 the same type. This means that the type of <literal>(?x, ?x)</literal>
895 is <literal>(?x::a) => (a,a)</literal>, and not
896 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
900 An implicit parameter is bound using the standard
901 <literal>let</literal> binding form, where the bindings must be a
902 collection of simple bindings to implicit-style variables (no
903 function-style bindings, and no type signatures); these bindings are
904 neither polymorphic or recursive. This form binds the implicit
905 parameters arising in the body, not the free variables as a
906 <literal>let</literal> or <literal>where</literal> would do. For
907 example, we define the <literal>min</literal> function by binding
908 <literal>cmp</literal>.</para>
911 min = let ?cmp = (<=) in least
914 Note the following additional constraints:
917 <para> You can't have an implicit parameter in the context of a class or instance
918 declaration. For example, both these declarations are illegal:
920 class (?x::Int) => C a where ...
921 instance (?x::a) => Foo [a] where ...
923 Reason: exactly which implicit parameter you pick up depends on exactly where
924 you invoke a function. But the ``invocation'' of instance declarations is done
925 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
926 Easiest thing is to outlaw the offending types.</para>
933 <sect2 id="linear-implicit-parameters">
934 <title>Linear implicit parameters
937 Linear implicit parameters are an idea developed by Koen Claessen,
938 Mark Shields, and Simon PJ. They address the long-standing
939 problem that monads seem over-kill for certain sorts of problem, notably:
942 <listitem> <para> distributing a supply of unique names </para> </listitem>
943 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
944 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
948 Linear implicit parameters are just like ordinary implicit parameters,
949 except that they are "linear" -- that is, they cannot be copied, and
950 must be explicitly "split" instead. Linear implicit parameters are
951 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
952 (The '/' in the '%' suggests the split!)
957 import GHC.Exts( Splittable )
959 data NameSupply = ...
961 splitNS :: NameSupply -> (NameSupply, NameSupply)
962 newName :: NameSupply -> Name
964 instance Splittable NameSupply where
968 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
969 f env (Lam x e) = Lam x' (f env e)
972 env' = extend env x x'
973 ...more equations for f...
975 Notice that the implicit parameter %ns is consumed
977 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
978 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
982 So the translation done by the type checker makes
983 the parameter explicit:
985 f :: NameSupply -> Env -> Expr -> Expr
986 f ns env (Lam x e) = Lam x' (f ns1 env e)
988 (ns1,ns2) = splitNS ns
990 env = extend env x x'
992 Notice the call to 'split' introduced by the type checker.
993 How did it know to use 'splitNS'? Because what it really did
994 was to introduce a call to the overloaded function 'split',
995 defined by the class <literal>Splittable</literal>:
997 class Splittable a where
1000 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
1001 split for name supplies. But we can simply write
1007 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
1009 The <literal>Splittable</literal> class is built into GHC. It's exported by module
1010 <literal>GHC.Exts</literal>.
1015 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
1016 are entirely distinct implicit parameters: you
1017 can use them together and they won't intefere with each other. </para>
1020 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
1022 <listitem> <para>You cannot have implicit parameters (whether linear or not)
1023 in the context of a class or instance declaration. </para></listitem>
1027 <sect3><title>Warnings</title>
1030 The monomorphism restriction is even more important than usual.
1031 Consider the example above:
1033 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1034 f env (Lam x e) = Lam x' (f env e)
1037 env' = extend env x x'
1039 If we replaced the two occurrences of x' by (newName %ns), which is
1040 usually a harmless thing to do, we get:
1042 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1043 f env (Lam x e) = Lam (newName %ns) (f env e)
1045 env' = extend env x (newName %ns)
1047 But now the name supply is consumed in <emphasis>three</emphasis> places
1048 (the two calls to newName,and the recursive call to f), so
1049 the result is utterly different. Urk! We don't even have
1053 Well, this is an experimental change. With implicit
1054 parameters we have already lost beta reduction anyway, and
1055 (as John Launchbury puts it) we can't sensibly reason about
1056 Haskell programs without knowing their typing.
1063 <sect2 id="functional-dependencies">
1064 <title>Functional dependencies
1067 <para> Functional dependencies are implemented as described by Mark Jones
1068 in "Type Classes with Functional Dependencies", Mark P. Jones,
1069 In Proceedings of the 9th European Symposium on Programming,
1070 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782.
1074 There should be more documentation, but there isn't (yet). Yell if you need it.
1079 <sect2 id="universal-quantification">
1080 <title>Arbitrary-rank polymorphism
1084 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
1085 allows us to say exactly what this means. For example:
1093 g :: forall b. (b -> b)
1095 The two are treated identically.
1099 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
1100 explicit universal quantification in
1102 For example, all the following types are legal:
1104 f1 :: forall a b. a -> b -> a
1105 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
1107 f2 :: (forall a. a->a) -> Int -> Int
1108 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
1110 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
1112 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
1113 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
1114 The <literal>forall</literal> makes explicit the universal quantification that
1115 is implicitly added by Haskell.
1118 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
1119 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
1120 shows, the polymorphic type on the left of the function arrow can be overloaded.
1123 The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
1124 they have rank-2 types on the left of a function arrow.
1127 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
1128 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
1129 that restriction has now been lifted.)
1130 In particular, a forall-type (also called a "type scheme"),
1131 including an operational type class context, is legal:
1133 <listitem> <para> On the left of a function arrow </para> </listitem>
1134 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
1135 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
1136 example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
1137 field type signatures.</para> </listitem>
1138 <listitem> <para> As the type of an implicit parameter </para> </listitem>
1139 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
1141 There is one place you cannot put a <literal>forall</literal>:
1142 you cannot instantiate a type variable with a forall-type. So you cannot
1143 make a forall-type the argument of a type constructor. So these types are illegal:
1145 x1 :: [forall a. a->a]
1146 x2 :: (forall a. a->a, Int)
1147 x3 :: Maybe (forall a. a->a)
1149 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
1150 a type variable any more!
1159 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
1160 the types of the constructor arguments. Here are several examples:
1166 data T a = T1 (forall b. b -> b -> b) a
1168 data MonadT m = MkMonad { return :: forall a. a -> m a,
1169 bind :: forall a b. m a -> (a -> m b) -> m b
1172 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
1178 The constructors have rank-2 types:
1184 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
1185 MkMonad :: forall m. (forall a. a -> m a)
1186 -> (forall a b. m a -> (a -> m b) -> m b)
1188 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
1194 Notice that you don't need to use a <literal>forall</literal> if there's an
1195 explicit context. For example in the first argument of the
1196 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
1197 prefixed to the argument type. The implicit <literal>forall</literal>
1198 quantifies all type variables that are not already in scope, and are
1199 mentioned in the type quantified over.
1203 As for type signatures, implicit quantification happens for non-overloaded
1204 types too. So if you write this:
1207 data T a = MkT (Either a b) (b -> b)
1210 it's just as if you had written this:
1213 data T a = MkT (forall b. Either a b) (forall b. b -> b)
1216 That is, since the type variable <literal>b</literal> isn't in scope, it's
1217 implicitly universally quantified. (Arguably, it would be better
1218 to <emphasis>require</emphasis> explicit quantification on constructor arguments
1219 where that is what is wanted. Feedback welcomed.)
1223 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
1224 the constructor to suitable values, just as usual. For example,
1235 a3 = MkSwizzle reverse
1238 a4 = let r x = Just x
1245 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1246 mkTs f x y = [T1 f x, T1 f y]
1252 The type of the argument can, as usual, be more general than the type
1253 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
1254 does not need the <literal>Ord</literal> constraint.)
1258 When you use pattern matching, the bound variables may now have
1259 polymorphic types. For example:
1265 f :: T a -> a -> (a, Char)
1266 f (T1 w k) x = (w k x, w 'c' 'd')
1268 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
1269 g (MkSwizzle s) xs f = s (map f (s xs))
1271 h :: MonadT m -> [m a] -> m [a]
1272 h m [] = return m []
1273 h m (x:xs) = bind m x $ \y ->
1274 bind m (h m xs) $ \ys ->
1281 In the function <function>h</function> we use the record selectors <literal>return</literal>
1282 and <literal>bind</literal> to extract the polymorphic bind and return functions
1283 from the <literal>MonadT</literal> data structure, rather than using pattern
1289 <title>Type inference</title>
1292 In general, type inference for arbitrary-rank types is undecideable.
1293 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
1294 to get a decidable algorithm by requiring some help from the programmer.
1295 We do not yet have a formal specification of "some help" but the rule is this:
1298 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
1299 provides an explicit polymorphic type for x, or GHC's type inference will assume
1300 that x's type has no foralls in it</emphasis>.
1303 What does it mean to "provide" an explicit type for x? You can do that by
1304 giving a type signature for x directly, using a pattern type signature
1305 (<xref linkend="scoped-type-variables">), thus:
1307 \ f :: (forall a. a->a) -> (f True, f 'c')
1309 Alternatively, you can give a type signature to the enclosing
1310 context, which GHC can "push down" to find the type for the variable:
1312 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
1314 Here the type signature on the expression can be pushed inwards
1315 to give a type signature for f. Similarly, and more commonly,
1316 one can give a type signature for the function itself:
1318 h :: (forall a. a->a) -> (Bool,Char)
1319 h f = (f True, f 'c')
1321 You don't need to give a type signature if the lambda bound variable
1322 is a constructor argument. Here is an example we saw earlier:
1324 f :: T a -> a -> (a, Char)
1325 f (T1 w k) x = (w k x, w 'c' 'd')
1327 Here we do not need to give a type signature to <literal>w</literal>, because
1328 it is an argument of constructor <literal>T1</literal> and that tells GHC all
1335 <sect3 id="implicit-quant">
1336 <title>Implicit quantification</title>
1339 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
1340 user-written types, if and only if there is no explicit <literal>forall</literal>,
1341 GHC finds all the type variables mentioned in the type that are not already
1342 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
1346 f :: forall a. a -> a
1353 h :: forall b. a -> b -> b
1359 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
1362 f :: (a -> a) -> Int
1364 f :: forall a. (a -> a) -> Int
1366 f :: (forall a. a -> a) -> Int
1369 g :: (Ord a => a -> a) -> Int
1370 -- MEANS the illegal type
1371 g :: forall a. (Ord a => a -> a) -> Int
1373 g :: (forall a. Ord a => a -> a) -> Int
1375 The latter produces an illegal type, which you might think is silly,
1376 but at least the rule is simple. If you want the latter type, you
1377 can write your for-alls explicitly. Indeed, doing so is strongly advised
1383 <sect2 id="type-synonyms">
1384 <title>Liberalised type synonyms
1388 Type synonmys are like macros at the type level, and
1389 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1390 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1392 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1393 in a type synonym, thus:
1395 type Discard a = forall b. Show b => a -> b -> (a, String)
1400 g :: Discard Int -> (Int,Bool) -- A rank-2 type
1407 You can write an unboxed tuple in a type synonym:
1409 type Pr = (# Int, Int #)
1417 You can apply a type synonym to a forall type:
1419 type Foo a = a -> a -> Bool
1421 f :: Foo (forall b. b->b)
1423 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1425 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1430 You can apply a type synonym to a partially applied type synonym:
1432 type Generic i o = forall x. i x -> o x
1435 foo :: Generic Id []
1437 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1439 foo :: forall x. x -> [x]
1447 GHC currently does kind checking before expanding synonyms (though even that
1451 After expanding type synonyms, GHC does validity checking on types, looking for
1452 the following mal-formedness which isn't detected simply by kind checking:
1455 Type constructor applied to a type involving for-alls.
1458 Unboxed tuple on left of an arrow.
1461 Partially-applied type synonym.
1465 this will be rejected:
1467 type Pr = (# Int, Int #)
1472 because GHC does not allow unboxed tuples on the left of a function arrow.
1477 <title>For-all hoisting</title>
1479 It is often convenient to use generalised type synonyms at the right hand
1480 end of an arrow, thus:
1482 type Discard a = forall b. a -> b -> a
1484 g :: Int -> Discard Int
1487 Simply expanding the type synonym would give
1489 g :: Int -> (forall b. Int -> b -> Int)
1491 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1493 g :: forall b. Int -> Int -> b -> Int
1495 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1496 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1497 performs the transformation:</emphasis>
1499 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1501 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1503 (In fact, GHC tries to retain as much synonym information as possible for use in
1504 error messages, but that is a usability issue.) This rule applies, of course, whether
1505 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1506 valid way to write <literal>g</literal>'s type signature:
1508 g :: Int -> Int -> forall b. b -> Int
1514 <sect2 id="existential-quantification">
1515 <title>Existentially quantified data constructors
1519 The idea of using existential quantification in data type declarations
1520 was suggested by Laufer (I believe, thought doubtless someone will
1521 correct me), and implemented in Hope+. It's been in Lennart
1522 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
1523 proved very useful. Here's the idea. Consider the declaration:
1529 data Foo = forall a. MkFoo a (a -> Bool)
1536 The data type <literal>Foo</literal> has two constructors with types:
1542 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1549 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1550 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1551 For example, the following expression is fine:
1557 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1563 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1564 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1565 isUpper</function> packages a character with a compatible function. These
1566 two things are each of type <literal>Foo</literal> and can be put in a list.
1570 What can we do with a value of type <literal>Foo</literal>?. In particular,
1571 what happens when we pattern-match on <function>MkFoo</function>?
1577 f (MkFoo val fn) = ???
1583 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1584 are compatible, the only (useful) thing we can do with them is to
1585 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1592 f (MkFoo val fn) = fn val
1598 What this allows us to do is to package heterogenous values
1599 together with a bunch of functions that manipulate them, and then treat
1600 that collection of packages in a uniform manner. You can express
1601 quite a bit of object-oriented-like programming this way.
1604 <sect3 id="existential">
1605 <title>Why existential?
1609 What has this to do with <emphasis>existential</emphasis> quantification?
1610 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1616 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1622 But Haskell programmers can safely think of the ordinary
1623 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1624 adding a new existential quantification construct.
1630 <title>Type classes</title>
1633 An easy extension (implemented in <Command>hbc</Command>) is to allow
1634 arbitrary contexts before the constructor. For example:
1640 data Baz = forall a. Eq a => Baz1 a a
1641 | forall b. Show b => Baz2 b (b -> b)
1647 The two constructors have the types you'd expect:
1653 Baz1 :: forall a. Eq a => a -> a -> Baz
1654 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1660 But when pattern matching on <function>Baz1</function> the matched values can be compared
1661 for equality, and when pattern matching on <function>Baz2</function> the first matched
1662 value can be converted to a string (as well as applying the function to it).
1663 So this program is legal:
1670 f (Baz1 p q) | p == q = "Yes"
1672 f (Baz2 v fn) = show (fn v)
1678 Operationally, in a dictionary-passing implementation, the
1679 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1680 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1681 extract it on pattern matching.
1685 Notice the way that the syntax fits smoothly with that used for
1686 universal quantification earlier.
1692 <title>Restrictions</title>
1695 There are several restrictions on the ways in which existentially-quantified
1696 constructors can be use.
1705 When pattern matching, each pattern match introduces a new,
1706 distinct, type for each existential type variable. These types cannot
1707 be unified with any other type, nor can they escape from the scope of
1708 the pattern match. For example, these fragments are incorrect:
1716 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1717 is the result of <function>f1</function>. One way to see why this is wrong is to
1718 ask what type <function>f1</function> has:
1722 f1 :: Foo -> a -- Weird!
1726 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1731 f1 :: forall a. Foo -> a -- Wrong!
1735 The original program is just plain wrong. Here's another sort of error
1739 f2 (Baz1 a b) (Baz1 p q) = a==q
1743 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1744 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1745 from the two <function>Baz1</function> constructors.
1753 You can't pattern-match on an existentially quantified
1754 constructor in a <literal>let</literal> or <literal>where</literal> group of
1755 bindings. So this is illegal:
1759 f3 x = a==b where { Baz1 a b = x }
1763 You can only pattern-match
1764 on an existentially-quantified constructor in a <literal>case</literal> expression or
1765 in the patterns of a function definition.
1767 The reason for this restriction is really an implementation one.
1768 Type-checking binding groups is already a nightmare without
1769 existentials complicating the picture. Also an existential pattern
1770 binding at the top level of a module doesn't make sense, because it's
1771 not clear how to prevent the existentially-quantified type "escaping".
1772 So for now, there's a simple-to-state restriction. We'll see how
1780 You can't use existential quantification for <literal>newtype</literal>
1781 declarations. So this is illegal:
1785 newtype T = forall a. Ord a => MkT a
1789 Reason: a value of type <literal>T</literal> must be represented as a pair
1790 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
1791 That contradicts the idea that <literal>newtype</literal> should have no
1792 concrete representation. You can get just the same efficiency and effect
1793 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
1794 overloading involved, then there is more of a case for allowing
1795 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
1796 because the <literal>data</literal> version does carry an implementation cost,
1797 but single-field existentially quantified constructors aren't much
1798 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
1799 stands, unless there are convincing reasons to change it.
1807 You can't use <literal>deriving</literal> to define instances of a
1808 data type with existentially quantified data constructors.
1810 Reason: in most cases it would not make sense. For example:#
1813 data T = forall a. MkT [a] deriving( Eq )
1816 To derive <literal>Eq</literal> in the standard way we would need to have equality
1817 between the single component of two <function>MkT</function> constructors:
1821 (MkT a) == (MkT b) = ???
1824 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
1825 It's just about possible to imagine examples in which the derived instance
1826 would make sense, but it seems altogether simpler simply to prohibit such
1827 declarations. Define your own instances!
1839 <sect2 id="scoped-type-variables">
1840 <title>Scoped type variables
1844 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
1845 variable</emphasis>. For example
1851 f (xs::[a]) = ys ++ ys
1860 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
1861 This brings the type variable <literal>a</literal> into scope; it scopes over
1862 all the patterns and right hand sides for this equation for <function>f</function>.
1863 In particular, it is in scope at the type signature for <VarName>y</VarName>.
1867 Pattern type signatures are completely orthogonal to ordinary, separate
1868 type signatures. The two can be used independently or together.
1869 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
1870 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
1871 implicitly universally quantified. (If there are no type variables in
1872 scope, all type variables mentioned in the signature are universally
1873 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
1874 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
1875 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
1876 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
1877 it becomes possible to do so.
1881 Scoped type variables are implemented in both GHC and Hugs. Where the
1882 implementations differ from the specification below, those differences
1887 So much for the basic idea. Here are the details.
1891 <title>What a pattern type signature means</title>
1893 A type variable brought into scope by a pattern type signature is simply
1894 the name for a type. The restriction they express is that all occurrences
1895 of the same name mean the same type. For example:
1897 f :: [Int] -> Int -> Int
1898 f (xs::[a]) (y::a) = (head xs + y) :: a
1900 The pattern type signatures on the left hand side of
1901 <literal>f</literal> express the fact that <literal>xs</literal>
1902 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
1903 must have this same type. The type signature on the expression <literal>(head xs)</literal>
1904 specifies that this expression must have the same type <literal>a</literal>.
1905 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
1906 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
1907 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
1908 rules, which specified that a pattern-bound type variable should be universally quantified.)
1909 For example, all of these are legal:</para>
1912 t (x::a) (y::a) = x+y*2
1914 f (x::a) (y::b) = [x,y] -- a unifies with b
1916 g (x::a) = x + 1::Int -- a unifies with Int
1918 h x = let k (y::a) = [x,y] -- a is free in the
1919 in k x -- environment
1921 k (x::a) True = ... -- a unifies with Int
1922 k (x::Int) False = ...
1925 w (x::a) = x -- a unifies with [b]
1931 <title>Scope and implicit quantification</title>
1939 All the type variables mentioned in a pattern,
1940 that are not already in scope,
1941 are brought into scope by the pattern. We describe this set as
1942 the <emphasis>type variables bound by the pattern</emphasis>.
1945 f (x::a) = let g (y::(a,b)) = fst y
1949 The pattern <literal>(x::a)</literal> brings the type variable
1950 <literal>a</literal> into scope, as well as the term
1951 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
1952 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
1953 and brings into scope the type variable <literal>b</literal>.
1959 The type variable(s) bound by the pattern have the same scope
1960 as the term variable(s) bound by the pattern. For example:
1963 f (x::a) = <...rhs of f...>
1964 (p::b, q::b) = (1,2)
1965 in <...body of let...>
1967 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
1968 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
1969 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
1970 just like <literal>p</literal> and <literal>q</literal> do.
1971 Indeed, the newly bound type variables also scope over any ordinary, separate
1972 type signatures in the <literal>let</literal> group.
1979 The type variables bound by the pattern may be
1980 mentioned in ordinary type signatures or pattern
1981 type signatures anywhere within their scope.
1988 In ordinary type signatures, any type variable mentioned in the
1989 signature that is in scope is <emphasis>not</emphasis> universally quantified.
1997 Ordinary type signatures do not bring any new type variables
1998 into scope (except in the type signature itself!). So this is illegal:
2005 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2006 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2007 and that is an incorrect typing.
2014 The pattern type signature is a monotype:
2019 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2023 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2024 not to type schemes.
2028 There is no implicit universal quantification on pattern type signatures (in contrast to
2029 ordinary type signatures).
2039 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2040 scope over the methods defined in the <literal>where</literal> part. For example:
2054 (Not implemented in Hugs yet, Dec 98).
2065 <title>Result type signatures</title>
2073 The result type of a function can be given a signature,
2078 f (x::a) :: [a] = [x,x,x]
2082 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2083 result type. Sometimes this is the only way of naming the type variable
2088 f :: Int -> [a] -> [a]
2089 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2090 in \xs -> map g (reverse xs `zip` xs)
2102 Result type signatures are not yet implemented in Hugs.
2108 <title>Where a pattern type signature can occur</title>
2111 A pattern type signature can occur in any pattern. For example:
2116 A pattern type signature can be on an arbitrary sub-pattern, not
2121 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2130 Pattern type signatures, including the result part, can be used
2131 in lambda abstractions:
2134 (\ (x::a, y) :: a -> x)
2141 Pattern type signatures, including the result part, can be used
2142 in <literal>case</literal> expressions:
2146 case e of { (x::a, y) :: a -> x }
2154 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2155 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2156 token or a parenthesised type of some sort). To see why,
2157 consider how one would parse this:
2171 Pattern type signatures can bind existential type variables.
2176 data T = forall a. MkT [a]
2179 f (MkT [t::a]) = MkT t3
2192 Pattern type signatures
2193 can be used in pattern bindings:
2196 f x = let (y, z::a) = x in ...
2197 f1 x = let (y, z::Int) = x in ...
2198 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2199 f3 :: (b->b) = \x -> x
2202 In all such cases, the binding is not generalised over the pattern-bound
2203 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2204 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2205 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2206 In contrast, the binding
2211 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2212 in <literal>f4</literal>'s scope.
2222 <sect2 id="sec-kinding">
2223 <title>Explicitly-kinded quantification</title>
2226 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2227 to give the kind explicitly as (machine-checked) documentation,
2228 just as it is nice to give a type signature for a function. On some occasions,
2229 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2230 John Hughes had to define the data type:
2232 data Set cxt a = Set [a]
2233 | Unused (cxt a -> ())
2235 The only use for the <literal>Unused</literal> constructor was to force the correct
2236 kind for the type variable <literal>cxt</literal>.
2239 GHC now instead allows you to specify the kind of a type variable directly, wherever
2240 a type variable is explicitly bound. Namely:
2242 <listitem><para><literal>data</literal> declarations:
2244 data Set (cxt :: * -> *) a = Set [a]
2245 </Screen></para></listitem>
2246 <listitem><para><literal>type</literal> declarations:
2248 type T (f :: * -> *) = f Int
2249 </Screen></para></listitem>
2250 <listitem><para><literal>class</literal> declarations:
2252 class (Eq a) => C (f :: * -> *) a where ...
2253 </Screen></para></listitem>
2254 <listitem><para><literal>forall</literal>'s in type signatures:
2256 f :: forall (cxt :: * -> *). Set cxt Int
2257 </Screen></para></listitem>
2262 The parentheses are required. Some of the spaces are required too, to
2263 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2264 will get a parse error, because "<literal>::*->*</literal>" is a
2265 single lexeme in Haskell.
2269 As part of the same extension, you can put kind annotations in types
2272 f :: (Int :: *) -> Int
2273 g :: forall a. a -> (a :: *)
2277 atype ::= '(' ctype '::' kind ')
2279 The parentheses are required.
2284 <!-- ==================== End of type system extensions ================= -->
2287 <!-- ==================== ASSERTIONS ================= -->
2289 <sect1 id="sec-assertions">
2291 <indexterm><primary>Assertions</primary></indexterm>
2295 If you want to make use of assertions in your standard Haskell code, you
2296 could define a function like the following:
2302 assert :: Bool -> a -> a
2303 assert False x = error "assertion failed!"
2310 which works, but gives you back a less than useful error message --
2311 an assertion failed, but which and where?
2315 One way out is to define an extended <function>assert</function> function which also
2316 takes a descriptive string to include in the error message and
2317 perhaps combine this with the use of a pre-processor which inserts
2318 the source location where <function>assert</function> was used.
2322 Ghc offers a helping hand here, doing all of this for you. For every
2323 use of <function>assert</function> in the user's source:
2329 kelvinToC :: Double -> Double
2330 kelvinToC k = assert (k >= 0.0) (k+273.15)
2336 Ghc will rewrite this to also include the source location where the
2343 assert pred val ==> assertError "Main.hs|15" pred val
2349 The rewrite is only performed by the compiler when it spots
2350 applications of <function>Control.Exception.assert</function>, so you
2351 can still define and use your own versions of
2352 <function>assert</function>, should you so wish. If not, import
2353 <literal>Control.Exception</literal> to make use
2354 <function>assert</function> in your code.
2358 To have the compiler ignore uses of assert, use the compiler option
2359 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
2360 option</primary></indexterm> That is, expressions of the form
2361 <literal>assert pred e</literal> will be rewritten to
2362 <literal>e</literal>.
2366 Assertion failures can be caught, see the documentation for the
2367 <literal>Control.Exception</literal> library for the details.
2373 <sect1 id="syntax-extns">
2374 <title>Syntactic extensions</title>
2376 <!-- ====================== HIERARCHICAL MODULES ======================= -->
2378 <sect2 id="hierarchical-modules">
2379 <title>Hierarchical Modules</title>
2381 <para>GHC supports a small extension to the syntax of module
2382 names: a module name is allowed to contain a dot
2383 <literal>‘.’</literal>. This is also known as the
2384 “hierarchical module namespace” extension, because
2385 it extends the normally flat Haskell module namespace into a
2386 more flexible hierarchy of modules.</para>
2388 <para>A module name in the extended syntax consists of a
2389 sequence of components, each separated by a dot. When searching
2390 for an interface file (or a source file, in the case of GHCi or
2391 when using <option>--make</option>) for an imported module, GHC
2392 interprets the dot as a path separator. So for example, if a
2393 module <literal>A.B.C</literal> is imported, then for each
2394 directory <literal>D</literal> on the search path (see the
2395 <option>-i</option> option, <xref
2396 linkend="options-finding-imports">), GHC will look in the
2397 directory <literal>D/A/B</literal><footnote><para>On Windows,
2398 this would be <literal>D\A\B</literal>.</para></footnote> for an
2399 interface file called <filename>C.hi</filename> or a source file
2400 <filename>C.hs</filename> or <filename>C.lhs</filename>.</para>
2402 <para>Note that as far as the compiler is concerned, module
2403 names are always fully qualified; the hierarchy only has a
2404 special meaning when searching for interface files and source
2405 files in the filesystem. In particular, this means that the
2406 full module name must be given after the
2407 <literal>module</literal> keyword at the beginning of the
2408 module; for example, the module <literal>A.B.C</literal> must
2411 <programlisting>module A.B.C</programlisting>
2413 <para>GHC comes with a large collection of libraries arranged
2414 hierarchically; see the accompanying library documentation.
2415 There is an ongoing project to create and maintain a stable set
2416 of <quote>core</quote> libraries used by several Haskell
2417 compilers, and the libraries that GHC comes with represent the
2418 current status of that project. For more details, see <ulink
2419 url="http://www.haskell.org/~simonmar/libraries/libraries.html">.</ulink></para>
2423 <!-- ====================== PATTERN GUARDS ======================= -->
2425 <sect2 id="pattern-guards">
2426 <title>Pattern guards</title>
2429 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
2430 The discussion that follows is an abbreviated version of Simon Peyton Jones's original <ULink URL="http://research.microsoft.com/~simonpj/Haskell/guards.html">proposal</ULink>. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)
2434 Suppose we have an abstract data type of finite maps, with a
2438 lookup :: FiniteMap -> Int -> Maybe Int
2441 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
2442 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
2446 clunky env var1 var2 | ok1 && ok2 = val1 + val2
2447 | otherwise = var1 + var2
2449 m1 = lookup env var1
2450 m2 = lookup env var2
2451 ok1 = maybeToBool m1
2452 ok2 = maybeToBool m2
2453 val1 = expectJust m1
2454 val2 = expectJust m2
2458 The auxiliary functions are
2462 maybeToBool :: Maybe a -> Bool
2463 maybeToBool (Just x) = True
2464 maybeToBool Nothing = False
2466 expectJust :: Maybe a -> a
2467 expectJust (Just x) = x
2468 expectJust Nothing = error "Unexpected Nothing"
2472 What is <function>clunky</function> doing? The guard <literal>ok1 &&
2473 ok2</literal> checks that both lookups succeed, using
2474 <function>maybeToBool</function> to convert the <function>Maybe</function>
2475 types to booleans. The (lazily evaluated) <function>expectJust</function>
2476 calls extract the values from the results of the lookups, and binds the
2477 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
2478 respectively. If either lookup fails, then clunky takes the
2479 <literal>otherwise</literal> case and returns the sum of its arguments.
2483 This is certainly legal Haskell, but it is a tremendously verbose and
2484 un-obvious way to achieve the desired effect. Arguably, a more direct way
2485 to write clunky would be to use case expressions:
2489 clunky env var1 var1 = case lookup env var1 of
2491 Just val1 -> case lookup env var2 of
2493 Just val2 -> val1 + val2
2499 This is a bit shorter, but hardly better. Of course, we can rewrite any set
2500 of pattern-matching, guarded equations as case expressions; that is
2501 precisely what the compiler does when compiling equations! The reason that
2502 Haskell provides guarded equations is because they allow us to write down
2503 the cases we want to consider, one at a time, independently of each other.
2504 This structure is hidden in the case version. Two of the right-hand sides
2505 are really the same (<function>fail</function>), and the whole expression
2506 tends to become more and more indented.
2510 Here is how I would write clunky:
2514 clunky env var1 var1
2515 | Just val1 <- lookup env var1
2516 , Just val2 <- lookup env var2
2518 ...other equations for clunky...
2522 The semantics should be clear enough. The qualifers are matched in order.
2523 For a <literal><-</literal> qualifier, which I call a pattern guard, the
2524 right hand side is evaluated and matched against the pattern on the left.
2525 If the match fails then the whole guard fails and the next equation is
2526 tried. If it succeeds, then the appropriate binding takes place, and the
2527 next qualifier is matched, in the augmented environment. Unlike list
2528 comprehensions, however, the type of the expression to the right of the
2529 <literal><-</literal> is the same as the type of the pattern to its
2530 left. The bindings introduced by pattern guards scope over all the
2531 remaining guard qualifiers, and over the right hand side of the equation.
2535 Just as with list comprehensions, boolean expressions can be freely mixed
2536 with among the pattern guards. For example:
2547 Haskell's current guards therefore emerge as a special case, in which the
2548 qualifier list has just one element, a boolean expression.
2552 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
2554 <sect2 id="parallel-list-comprehensions">
2555 <title>Parallel List Comprehensions</title>
2556 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
2558 <indexterm><primary>parallel list comprehensions</primary>
2561 <para>Parallel list comprehensions are a natural extension to list
2562 comprehensions. List comprehensions can be thought of as a nice
2563 syntax for writing maps and filters. Parallel comprehensions
2564 extend this to include the zipWith family.</para>
2566 <para>A parallel list comprehension has multiple independent
2567 branches of qualifier lists, each separated by a `|' symbol. For
2568 example, the following zips together two lists:</para>
2571 [ (x, y) | x <- xs | y <- ys ]
2574 <para>The behavior of parallel list comprehensions follows that of
2575 zip, in that the resulting list will have the same length as the
2576 shortest branch.</para>
2578 <para>We can define parallel list comprehensions by translation to
2579 regular comprehensions. Here's the basic idea:</para>
2581 <para>Given a parallel comprehension of the form: </para>
2584 [ e | p1 <- e11, p2 <- e12, ...
2585 | q1 <- e21, q2 <- e22, ...
2590 <para>This will be translated to: </para>
2593 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
2594 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
2599 <para>where `zipN' is the appropriate zip for the given number of
2604 <sect2 id="rebindable-syntax">
2605 <title>Rebindable syntax</title>
2608 <para>GHC allows most kinds of built-in syntax to be rebound by
2609 the user, to facilitate replacing the <literal>Prelude</literal>
2610 with a home-grown version, for example.</para>
2612 <para>You may want to define your own numeric class
2613 hierarchy. It completely defeats that purpose if the
2614 literal "1" means "<literal>Prelude.fromInteger
2615 1</literal>", which is what the Haskell Report specifies.
2616 So the <option>-fno-implicit-prelude</option> flag causes
2617 the following pieces of built-in syntax to refer to
2618 <emphasis>whatever is in scope</emphasis>, not the Prelude
2623 <para>Integer and fractional literals mean
2624 "<literal>fromInteger 1</literal>" and
2625 "<literal>fromRational 3.2</literal>", not the
2626 Prelude-qualified versions; both in expressions and in
2631 <para>Negation (e.g. "<literal>- (f x)</literal>")
2632 means "<literal>negate (f x)</literal>" (not
2633 <literal>Prelude.negate</literal>).</para>
2637 <para>In an n+k pattern, the standard Prelude
2638 <literal>Ord</literal> class is still used for comparison,
2639 but the necessary subtraction uses whatever
2640 "<literal>(-)</literal>" is in scope (not
2641 "<literal>Prelude.(-)</literal>").</para>
2645 <para>"Do" notation is translated using whatever
2646 functions <literal>(>>=)</literal>,
2647 <literal>(>>)</literal>, <literal>fail</literal>, and
2648 <literal>return</literal>, are in scope (not the Prelude
2649 versions). List comprehensions, and parallel array
2650 comprehensions, are unaffected. </para></listitem>
2653 <para>Be warned: this is an experimental facility, with fewer checks than
2654 usual. In particular, it is essential that the functions GHC finds in scope
2655 must have the appropriate types, namely:
2657 fromInteger :: forall a. (...) => Integer -> a
2658 fromRational :: forall a. (...) => Rational -> a
2659 negate :: forall a. (...) => a -> a
2660 (-) :: forall a. (...) => a -> a -> a
2661 (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b
2662 (>>) :: forall m a. (...) => m a -> m b -> m b
2663 return :: forall m a. (...) => a -> m a
2664 fail :: forall m a. (...) => String -> m a
2666 (The (...) part can be any context including the empty context; that part
2668 If the functions don't have the right type, very peculiar things may
2669 happen. Use <literal>-dcore-lint</literal> to
2670 typecheck the desugared program. If Core Lint is happy you should be all right.</para>
2675 <!-- =============================== PRAGMAS =========================== -->
2677 <sect1 id="pragmas">
2678 <title>Pragmas</title>
2680 <indexterm><primary>pragma</primary></indexterm>
2682 <para>GHC supports several pragmas, or instructions to the
2683 compiler placed in the source code. Pragmas don't normally affect
2684 the meaning of the program, but they might affect the efficiency
2685 of the generated code.</para>
2687 <para>Pragmas all take the form
2689 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
2691 where <replaceable>word</replaceable> indicates the type of
2692 pragma, and is followed optionally by information specific to that
2693 type of pragma. Case is ignored in
2694 <replaceable>word</replaceable>. The various values for
2695 <replaceable>word</replaceable> that GHC understands are described
2696 in the following sections; any pragma encountered with an
2697 unrecognised <replaceable>word</replaceable> is (silently)
2700 <sect2 id="inline-pragma">
2701 <title>INLINE pragma
2703 <indexterm><primary>INLINE pragma</primary></indexterm>
2704 <indexterm><primary>pragma, INLINE</primary></indexterm></title>
2707 GHC (with <option>-O</option>, as always) tries to inline (or “unfold”)
2708 functions/values that are “small enough,” thus avoiding the call
2709 overhead and possibly exposing other more-wonderful optimisations.
2713 You will probably see these unfoldings (in Core syntax) in your
2718 Normally, if GHC decides a function is “too expensive” to inline, it
2719 will not do so, nor will it export that unfolding for other modules to
2724 The sledgehammer you can bring to bear is the
2725 <literal>INLINE</literal><indexterm><primary>INLINE pragma</primary></indexterm> pragma, used thusly:
2728 key_function :: Int -> String -> (Bool, Double)
2730 #ifdef __GLASGOW_HASKELL__
2731 {-# INLINE key_function #-}
2735 (You don't need to do the C pre-processor carry-on unless you're going
2736 to stick the code through HBC—it doesn't like <literal>INLINE</literal> pragmas.)
2740 The major effect of an <literal>INLINE</literal> pragma is to declare a function's
2741 “cost” to be very low. The normal unfolding machinery will then be
2742 very keen to inline it.
2746 An <literal>INLINE</literal> pragma for a function can be put anywhere its type
2747 signature could be put.
2751 <literal>INLINE</literal> pragmas are a particularly good idea for the
2752 <literal>then</literal>/<literal>return</literal> (or <literal>bind</literal>/<literal>unit</literal>) functions in a monad.
2753 For example, in GHC's own <literal>UniqueSupply</literal> monad code, we have:
2756 #ifdef __GLASGOW_HASKELL__
2757 {-# INLINE thenUs #-}
2758 {-# INLINE returnUs #-}
2766 <sect2 id="noinline-pragma">
2767 <title>NOINLINE pragma
2770 <indexterm><primary>NOINLINE pragma</primary></indexterm>
2771 <indexterm><primary>pragma</primary><secondary>NOINLINE</secondary></indexterm>
2772 <indexterm><primary>NOTINLINE pragma</primary></indexterm>
2773 <indexterm><primary>pragma</primary><secondary>NOTINLINE</secondary></indexterm>
2776 The <literal>NOINLINE</literal> pragma does exactly what you'd expect:
2777 it stops the named function from being inlined by the compiler. You
2778 shouldn't ever need to do this, unless you're very cautious about code
2782 <para><literal>NOTINLINE</literal> is a synonym for
2783 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is specified
2784 by Haskell 98 as the standard way to disable inlining, so it should be
2785 used if you want your code to be portable).</para>
2789 <sect2 id="specialize-pragma">
2790 <title>SPECIALIZE pragma</title>
2792 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2793 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
2794 <indexterm><primary>overloading, death to</primary></indexterm>
2796 <para>(UK spelling also accepted.) For key overloaded
2797 functions, you can create extra versions (NB: more code space)
2798 specialised to particular types. Thus, if you have an
2799 overloaded function:</para>
2802 hammeredLookup :: Ord key => [(key, value)] -> key -> value
2805 <para>If it is heavily used on lists with
2806 <literal>Widget</literal> keys, you could specialise it as
2810 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
2813 <para>To get very fancy, you can also specify a named function
2814 to use for the specialised value, as in:</para>
2817 {-# RULES hammeredLookup = blah #-}
2820 <para>where <literal>blah</literal> is an implementation of
2821 <literal>hammerdLookup</literal> written specialy for
2822 <literal>Widget</literal> lookups. It's <emphasis>Your
2823 Responsibility</emphasis> to make sure that
2824 <function>blah</function> really behaves as a specialised
2825 version of <function>hammeredLookup</function>!!!</para>
2827 <para>Note we use the <literal>RULE</literal> pragma here to
2828 indicate that <literal>hammeredLookup</literal> applied at a
2829 certain type should be replaced by <literal>blah</literal>. See
2830 <xref linkend="rules"> for more information on
2831 <literal>RULES</literal>.</para>
2833 <para>An example in which using <literal>RULES</literal> for
2834 specialisation will Win Big:
2837 toDouble :: Real a => a -> Double
2838 toDouble = fromRational . toRational
2840 {-# SPECIALIZE toDouble :: Int -> Double = i2d #-}
2841 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
2844 The <function>i2d</function> function is virtually one machine
2845 instruction; the default conversion—via an intermediate
2846 <literal>Rational</literal>—is obscenely expensive by
2849 <para>A <literal>SPECIALIZE</literal> pragma for a function can
2850 be put anywhere its type signature could be put.</para>
2854 <sect2 id="specialize-instance-pragma">
2855 <title>SPECIALIZE instance pragma
2859 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2860 <indexterm><primary>overloading, death to</primary></indexterm>
2861 Same idea, except for instance declarations. For example:
2864 instance (Eq a) => Eq (Foo a) where {
2865 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
2869 The pragma must occur inside the <literal>where</literal> part
2870 of the instance declaration.
2873 Compatible with HBC, by the way, except perhaps in the placement
2879 <sect2 id="line-pragma">
2884 <indexterm><primary>LINE pragma</primary></indexterm>
2885 <indexterm><primary>pragma, LINE</primary></indexterm>
2889 This pragma is similar to C's <literal>#line</literal> pragma, and is mainly for use in
2890 automatically generated Haskell code. It lets you specify the line
2891 number and filename of the original code; for example
2897 {-# LINE 42 "Foo.vhs" #-}
2903 if you'd generated the current file from something called <filename>Foo.vhs</filename>
2904 and this line corresponds to line 42 in the original. GHC will adjust
2905 its error messages to refer to the line/file named in the <literal>LINE</literal>
2912 <title>RULES pragma</title>
2915 The RULES pragma lets you specify rewrite rules. It is described in
2916 <xref LinkEnd="rewrite-rules">.
2921 <sect2 id="deprecated-pragma">
2922 <title>DEPRECATED pragma</title>
2925 The DEPRECATED pragma lets you specify that a particular function, class, or type, is deprecated.
2926 There are two forms.
2930 You can deprecate an entire module thus:</para>
2932 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
2936 When you compile any module that import <literal>Wibble</literal>, GHC will print
2937 the specified message.</para>
2942 You can deprecate a function, class, or type, with the following top-level declaration:
2945 {-# DEPRECATED f, C, T "Don't use these" #-}
2948 When you compile any module that imports and uses any of the specifed entities,
2949 GHC will print the specified message.
2953 <para>You can suppress the warnings with the flag <option>-fno-warn-deprecations</option>.</para>
2959 <!-- ======================= REWRITE RULES ======================== -->
2961 <sect1 id="rewrite-rules">
2962 <title>Rewrite rules
2964 <indexterm><primary>RULES pagma</primary></indexterm>
2965 <indexterm><primary>pragma, RULES</primary></indexterm>
2966 <indexterm><primary>rewrite rules</primary></indexterm></title>
2969 The programmer can specify rewrite rules as part of the source program
2970 (in a pragma). GHC applies these rewrite rules wherever it can.
2978 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
2985 <title>Syntax</title>
2988 From a syntactic point of view:
2994 Each rule has a name, enclosed in double quotes. The name itself has
2995 no significance at all. It is only used when reporting how many times the rule fired.
3001 There may be zero or more rules in a <literal>RULES</literal> pragma.
3007 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
3008 is set, so you must lay out your rules starting in the same column as the
3009 enclosing definitions.
3015 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
3016 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
3017 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
3018 by spaces, just like in a type <literal>forall</literal>.
3024 A pattern variable may optionally have a type signature.
3025 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
3026 For example, here is the <literal>foldr/build</literal> rule:
3029 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
3030 foldr k z (build g) = g k z
3033 Since <function>g</function> has a polymorphic type, it must have a type signature.
3040 The left hand side of a rule must consist of a top-level variable applied
3041 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
3044 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
3045 "wrong2" forall f. f True = True
3048 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
3055 A rule does not need to be in the same module as (any of) the
3056 variables it mentions, though of course they need to be in scope.
3062 Rules are automatically exported from a module, just as instance declarations are.
3073 <title>Semantics</title>
3076 From a semantic point of view:
3082 Rules are only applied if you use the <option>-O</option> flag.
3088 Rules are regarded as left-to-right rewrite rules.
3089 When GHC finds an expression that is a substitution instance of the LHS
3090 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
3091 By "a substitution instance" we mean that the LHS can be made equal to the
3092 expression by substituting for the pattern variables.
3099 The LHS and RHS of a rule are typechecked, and must have the
3107 GHC makes absolutely no attempt to verify that the LHS and RHS
3108 of a rule have the same meaning. That is undecideable in general, and
3109 infeasible in most interesting cases. The responsibility is entirely the programmer's!
3116 GHC makes no attempt to make sure that the rules are confluent or
3117 terminating. For example:
3120 "loop" forall x,y. f x y = f y x
3123 This rule will cause the compiler to go into an infinite loop.
3130 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
3136 GHC currently uses a very simple, syntactic, matching algorithm
3137 for matching a rule LHS with an expression. It seeks a substitution
3138 which makes the LHS and expression syntactically equal modulo alpha
3139 conversion. The pattern (rule), but not the expression, is eta-expanded if
3140 necessary. (Eta-expanding the epression can lead to laziness bugs.)
3141 But not beta conversion (that's called higher-order matching).
3145 Matching is carried out on GHC's intermediate language, which includes
3146 type abstractions and applications. So a rule only matches if the
3147 types match too. See <xref LinkEnd="rule-spec"> below.
3153 GHC keeps trying to apply the rules as it optimises the program.
3154 For example, consider:
3163 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
3164 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
3165 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
3166 not be substituted, and the rule would not fire.
3173 In the earlier phases of compilation, GHC inlines <emphasis>nothing
3174 that appears on the LHS of a rule</emphasis>, because once you have substituted
3175 for something you can't match against it (given the simple minded
3176 matching). So if you write the rule
3179 "map/map" forall f,g. map f . map g = map (f.g)
3182 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
3183 It will only match something written with explicit use of ".".
3184 Well, not quite. It <emphasis>will</emphasis> match the expression
3190 where <function>wibble</function> is defined:
3193 wibble f g = map f . map g
3196 because <function>wibble</function> will be inlined (it's small).
3198 Later on in compilation, GHC starts inlining even things on the
3199 LHS of rules, but still leaves the rules enabled. This inlining
3200 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
3207 All rules are implicitly exported from the module, and are therefore
3208 in force in any module that imports the module that defined the rule, directly
3209 or indirectly. (That is, if A imports B, which imports C, then C's rules are
3210 in force when compiling A.) The situation is very similar to that for instance
3222 <title>List fusion</title>
3225 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
3226 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
3227 intermediate list should be eliminated entirely.
3231 The following are good producers:
3243 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
3249 Explicit lists (e.g. <literal>[True, False]</literal>)
3255 The cons constructor (e.g <literal>3:4:[]</literal>)
3261 <function>++</function>
3267 <function>map</function>
3273 <function>filter</function>
3279 <function>iterate</function>, <function>repeat</function>
3285 <function>zip</function>, <function>zipWith</function>
3294 The following are good consumers:
3306 <function>array</function> (on its second argument)
3312 <function>length</function>
3318 <function>++</function> (on its first argument)
3324 <function>foldr</function>
3330 <function>map</function>
3336 <function>filter</function>
3342 <function>concat</function>
3348 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
3354 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
3355 will fuse with one but not the other)
3361 <function>partition</function>
3367 <function>head</function>
3373 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
3379 <function>sequence_</function>
3385 <function>msum</function>
3391 <function>sortBy</function>
3400 So, for example, the following should generate no intermediate lists:
3403 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
3409 This list could readily be extended; if there are Prelude functions that you use
3410 a lot which are not included, please tell us.
3414 If you want to write your own good consumers or producers, look at the
3415 Prelude definitions of the above functions to see how to do so.
3420 <sect2 id="rule-spec">
3421 <title>Specialisation
3425 Rewrite rules can be used to get the same effect as a feature
3426 present in earlier version of GHC:
3429 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
3432 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
3433 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
3434 specialising the original definition of <function>fromIntegral</function> the programmer is
3435 promising that it is safe to use <function>int8ToInt16</function> instead.
3439 This feature is no longer in GHC. But rewrite rules let you do the
3444 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
3448 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
3449 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
3450 GHC adds the type and dictionary applications to get the typed rule
3453 forall (d1::Integral Int8) (d2::Num Int16) .
3454 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
3458 this rule does not need to be in the same file as fromIntegral,
3459 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
3460 have an original definition available to specialise).
3466 <title>Controlling what's going on</title>
3474 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
3480 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
3481 If you add <option>-dppr-debug</option> you get a more detailed listing.
3487 The defintion of (say) <function>build</function> in <FileName>PrelBase.lhs</FileName> looks llike this:
3490 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
3491 {-# INLINE build #-}
3495 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
3496 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
3497 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
3498 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
3505 In <filename>ghc/lib/std/PrelBase.lhs</filename> look at the rules for <function>map</function> to
3506 see how to write rules that will do fusion and yet give an efficient
3507 program even if fusion doesn't happen. More rules in <filename>PrelList.lhs</filename>.
3519 <sect1 id="generic-classes">
3520 <title>Generic classes</title>
3522 <para>(Note: support for generic classes is currently broken in
3526 The ideas behind this extension are described in detail in "Derivable type classes",
3527 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
3528 An example will give the idea:
3536 fromBin :: [Int] -> (a, [Int])
3538 toBin {| Unit |} Unit = []
3539 toBin {| a :+: b |} (Inl x) = 0 : toBin x
3540 toBin {| a :+: b |} (Inr y) = 1 : toBin y
3541 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
3543 fromBin {| Unit |} bs = (Unit, bs)
3544 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
3545 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
3546 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
3547 (y,bs'') = fromBin bs'
3550 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
3551 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
3552 which are defined thus in the library module <literal>Generics</literal>:
3556 data a :+: b = Inl a | Inr b
3557 data a :*: b = a :*: b
3560 Now you can make a data type into an instance of Bin like this:
3562 instance (Bin a, Bin b) => Bin (a,b)
3563 instance Bin a => Bin [a]
3565 That is, just leave off the "where" clasuse. Of course, you can put in the
3566 where clause and over-ride whichever methods you please.
3570 <title> Using generics </title>
3571 <para>To use generics you need to</para>
3574 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
3575 <option>-fgenerics</option> (to generate extra per-data-type code),
3576 and <option>-package lang</option> (to make the <literal>Generics</literal> library
3580 <para>Import the module <literal>Generics</literal> from the
3581 <literal>lang</literal> package. This import brings into
3582 scope the data types <literal>Unit</literal>,
3583 <literal>:*:</literal>, and <literal>:+:</literal>. (You
3584 don't need this import if you don't mention these types
3585 explicitly; for example, if you are simply giving instance
3586 declarations.)</para>
3591 <sect2> <title> Changes wrt the paper </title>
3593 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
3594 can be written infix (indeed, you can now use
3595 any operator starting in a colon as an infix type constructor). Also note that
3596 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
3597 Finally, note that the syntax of the type patterns in the class declaration
3598 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
3599 alone would ambiguous when they appear on right hand sides (an extension we
3600 anticipate wanting).
3604 <sect2> <title>Terminology and restrictions</title>
3606 Terminology. A "generic default method" in a class declaration
3607 is one that is defined using type patterns as above.
3608 A "polymorphic default method" is a default method defined as in Haskell 98.
3609 A "generic class declaration" is a class declaration with at least one
3610 generic default method.
3618 Alas, we do not yet implement the stuff about constructor names and
3625 A generic class can have only one parameter; you can't have a generic
3626 multi-parameter class.
3632 A default method must be defined entirely using type patterns, or entirely
3633 without. So this is illegal:
3636 op :: a -> (a, Bool)
3637 op {| Unit |} Unit = (Unit, True)
3640 However it is perfectly OK for some methods of a generic class to have
3641 generic default methods and others to have polymorphic default methods.
3647 The type variable(s) in the type pattern for a generic method declaration
3648 scope over the right hand side. So this is legal (note the use of the type variable ``p'' in a type signature on the right hand side:
3652 op {| p :*: q |} (x :*: y) = op (x :: p)
3660 The type patterns in a generic default method must take one of the forms:
3666 where "a" and "b" are type variables. Furthermore, all the type patterns for
3667 a single type constructor (<literal>:*:</literal>, say) must be identical; they
3668 must use the same type variables. So this is illegal:
3672 op {| a :+: b |} (Inl x) = True
3673 op {| p :+: q |} (Inr y) = False
3675 The type patterns must be identical, even in equations for different methods of the class.
3676 So this too is illegal:
3680 op1 {| a :*: b |} (x :*: y) = True
3683 op2 {| p :*: q |} (x :*: y) = False
3685 (The reason for this restriction is that we gather all the equations for a particular type consructor
3686 into a single generic instance declaration.)
3692 A generic method declaration must give a case for each of the three type constructors.
3698 The type for a generic method can be built only from:
3700 <listitem> <para> Function arrows </para> </listitem>
3701 <listitem> <para> Type variables </para> </listitem>
3702 <listitem> <para> Tuples </para> </listitem>
3703 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
3705 Here are some example type signatures for generic methods:
3708 op2 :: Bool -> (a,Bool)
3709 op3 :: [Int] -> a -> a
3712 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
3716 This restriction is an implementation restriction: we just havn't got around to
3717 implementing the necessary bidirectional maps over arbitrary type constructors.
3718 It would be relatively easy to add specific type constructors, such as Maybe and list,
3719 to the ones that are allowed.</para>
3724 In an instance declaration for a generic class, the idea is that the compiler
3725 will fill in the methods for you, based on the generic templates. However it can only
3730 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
3735 No constructor of the instance type has unboxed fields.
3739 (Of course, these things can only arise if you are already using GHC extensions.)
3740 However, you can still give an instance declarations for types which break these rules,
3741 provided you give explicit code to override any generic default methods.
3749 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
3750 what the compiler does with generic declarations.
3755 <sect2> <title> Another example </title>
3757 Just to finish with, here's another example I rather like:
3761 nCons {| Unit |} _ = 1
3762 nCons {| a :*: b |} _ = 1
3763 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
3766 tag {| Unit |} _ = 1
3767 tag {| a :*: b |} _ = 1
3768 tag {| a :+: b |} (Inl x) = tag x
3769 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
3775 <sect1 id="newtype-deriving">
3776 <title>Generalised derived instances for newtypes</title>
3779 When you define an abstract type using <literal>newtype</literal>, you may want
3780 the new type to inherit some instances from its representation. In
3781 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3782 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3783 other classes you have to write an explicit instance declaration. For
3784 example, if you define
3787 newtype Dollars = Dollars Int
3790 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3791 explicitly define an instance of <literal>Num</literal>:
3794 instance Num Dollars where
3795 Dollars a + Dollars b = Dollars (a+b)
3798 All the instance does is apply and remove the <literal>newtype</literal>
3799 constructor. It is particularly galling that, since the constructor
3800 doesn't appear at run-time, this instance declaration defines a
3801 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3802 dictionary, only slower!
3805 <sect2> <title> Generalising the deriving clause </title>
3807 GHC now permits such instances to be derived instead, so one can write
3809 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3812 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3813 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3814 derives an instance declaration of the form
3817 instance Num Int => Num Dollars
3820 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3824 We can also derive instances of constructor classes in a similar
3825 way. For example, suppose we have implemented state and failure monad
3826 transformers, such that
3829 instance Monad m => Monad (State s m)
3830 instance Monad m => Monad (Failure m)
3832 In Haskell 98, we can define a parsing monad by
3834 type Parser tok m a = State [tok] (Failure m) a
3837 which is automatically a monad thanks to the instance declarations
3838 above. With the extension, we can make the parser type abstract,
3839 without needing to write an instance of class <literal>Monad</literal>, via
3842 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3845 In this case the derived instance declaration is of the form
3847 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3850 Notice that, since <literal>Monad</literal> is a constructor class, the
3851 instance is a <emphasis>partial application</emphasis> of the new type, not the
3852 entire left hand side. We can imagine that the type declaration is
3853 ``eta-converted'' to generate the context of the instance
3858 We can even derive instances of multi-parameter classes, provided the
3859 newtype is the last class parameter. In this case, a ``partial
3860 application'' of the class appears in the <literal>deriving</literal>
3861 clause. For example, given the class
3864 class StateMonad s m | m -> s where ...
3865 instance Monad m => StateMonad s (State s m) where ...
3867 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3869 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3870 deriving (Monad, StateMonad [tok])
3873 The derived instance is obtained by completing the application of the
3874 class to the new type:
3877 instance StateMonad [tok] (State [tok] (Failure m)) =>
3878 StateMonad [tok] (Parser tok m)
3883 As a result of this extension, all derived instances in newtype
3884 declarations are treated uniformly (and implemented just by reusing
3885 the dictionary for the representation type), <emphasis>except</emphasis>
3886 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3887 the newtype and its representation.
3891 <sect2> <title> A more precise specification </title>
3893 Derived instance declarations are constructed as follows. Consider the
3894 declaration (after expansion of any type synonyms)
3897 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3900 where <literal>S</literal> is a type constructor, <literal>t1...tk</literal> are
3902 <literal>vk+1...vn</literal> are type variables which do not occur in any of
3903 the <literal>ti</literal>, and the <literal>ci</literal> are partial applications of
3904 classes of the form <literal>C t1'...tj'</literal>. The derived instance
3905 declarations are, for each <literal>ci</literal>,
3908 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3910 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3911 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3915 As an example which does <emphasis>not</emphasis> work, consider
3917 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3919 Here we cannot derive the instance
3921 instance Monad (State s m) => Monad (NonMonad m)
3924 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3925 and so cannot be "eta-converted" away. It is a good thing that this
3926 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3927 not, in fact, a monad --- for the same reason. Try defining
3928 <literal>>>=</literal> with the correct type: you won't be able to.
3932 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3933 important, since we can only derive instances for the last one. If the
3934 <literal>StateMonad</literal> class above were instead defined as
3937 class StateMonad m s | m -> s where ...
3940 then we would not have been able to derive an instance for the
3941 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3942 classes usually have one "main" parameter for which deriving new
3943 instances is most interesting.
3951 ;;; Local Variables: ***
3953 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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